Integrate the function
Answers
Step-by-step explanation:
f(x) = (sin x)2 can be written as f(u) = u2 where u = sin x. The Chain Rule states that to differentiate a composite function we differentiate the outer function and multiply by the derivative of the inner function. We can use the rules cos x = sin ( /2– x) and sin x = cos( /2 – x) to find the derivative of cos x.Explanation:
y
=
sin
(
x
2
)
Applying the chain rule:
d
y
d
x
=
cos
(
x
2
)
⋅
d
d
x
(
x
2
)
=
cos
(
x
2
)
⋅
2
x
[Power rule]
=
2
x
cos
(
x
2
)
Step-by-step explanation:
Biodiversity is the variety and variability of life on Earth. Biodiversity is typically a measure of variation at the genetic, species, and ecosystem level. Terrestrial biodiversity is usually greater near the equator, which is the result of the warm climate and high primary productivity. Biodiversity is not distributed evenly on Earth, and is richer in the tropics. These tropical forest ecosystems cover less than 10 percent of earth's surface, and contain about 90 percent of the world's species. Marine biodiversity is usually higher along coasts in the Western Pacific, where sea surface temperature is highest, and in the mid-latitudinal band in all oceans. There are latitudinal gradients in species diversity. Biodiversity generally tends to cluster in hotspots, and has been increasing through time, but will be likely to slow in the future.